Large-Scale Analysis of Changing Frequencies of Rain-On-Snow Events with ﬂood-Generation Potential

Hydrol. Earth Syst. Sci., 18, 2695–2709, 2014 www.hydrol-earth-syst-sci.net/18/2695/2014/ doi:10.5194/hess-18-2695-2014 © Author(s) 2014. CC Attribution 3.0 License.

Large-scale analysis of changing frequencies of rain-on-snow events with ﬂood-generation potential

D. Freudiger, I. Kohn, K. Stahl, and M. Weiler Chair of Hydrology, University of Freiburg, Freiburg, Germany

Correspondence to: D. Freudiger ([email protected])

Received: 18 September 2013 – Published in Hydrol. Earth Syst. Sci. Discuss.: 5 November 2013 Revised: 21 May 2014 – Accepted: 27 May 2014 – Published: 24 July 2014

Abstract. In January 2011 a rain-on-snow (RoS) event 1 Introduction caused floods in the major river basins in central Europe, i.e. the Rhine, Danube, Weser, Elbe, Oder, and Ems. This event Rain-on-snow (RoS) events are relevant for water resources prompted the questions of how to define a RoS event and management, particularly for flood forecasting and flood risk whether those events have become more frequent. Based on management (McCabe et al., 2007). RoS events have the the flood of January 2011 and on other known events of the potential to cause large flood events during the winter sea- past, threshold values for potentially flood-generating RoS son. They represent one of five flood process types defined events were determined. Consequently events with rainfall by Merz and Blöschl (2003) that occur in temperate-climate of at least 3 mm on a snowpack of at least 10 mm snow wa- mountain river systems and are strongly elevation dependent. ter equivalent (SWE) and for which the sum of rainfall and These events are complex as they do not only depend on the snowmelt contains a minimum of 20 % snowmelt were anal- rain intensity and amount, but also on the prevailing freez- ysed. RoS events were estimated for the time period 1950– ing level, the snow water equivalent (SWE), the snow en- 2011 and for the entire study area based on a temperature ergy content, the timing of release, and the areal extent of the index snow model driven with a European-scale gridded data snowpack (Kattelmann, 1997; McCabe et al., 2007). Snow- set of daily climate (E-OBS data). Frequencies and magni- packs are water reservoirs of large regional extent and storage tudes of the modelled events differ depending on the eleva- capacity, which can produce rapid melt in combination with tion range. When distinguishing alpine, upland, and lowland warm air temperatures and high humidity (e.g. Singh et al., basins, we found that upland basins are most influenced by 1997; Marks et al., 1998). Consequently, cumulative rainfall RoS events. Overall, the frequency of rainfall increased dur- and snowmelt can increase the magnitude of runoff and can ing winter, while the frequency of snowfall decreased during thus generate much greater potential for flooding than a usual spring. A decrease in the frequency of RoS events from April snowmelt event (Kattelmann, 1985; Marks et al., 1998). Be- to May has been observed in all upland basins since 1990. In sides their large damage potential, such events are also very contrast, the results suggest an increasing trend in the magni- difficult to forecast as shown by Rössler et al. (2014) for a tude and frequency of RoS days in January and February for RoS-driven flood event in October 2011 in the Bernese Alps most of the lowland and upland basins. These results suggest in Switzerland. Scientific interest has therefore increased in that the flood hazard from RoS events in the early winter sea- the last decades, and a number of different methods of analy- son has increased in the medium-elevation mountain ranges sis have been developed to better understand and quantify the of central Europe, especially in the Rhine, Weser, and Elbe physical processes by studying individual events in different river basins. locations (e.g. Blöschl et al., 1990; Singh et al., 1997; Floyd and Weiler, 2008; Garvelmann et al., 2013). Many studies observed an increase in the occurrence of rainfall in the wintertime and a trend to earlier snowmelt due to an increase of air temperatures in Europe (e.g. Birsan et al., 2005; Renard et al., 2008). Furthermore, Köplin et al. (2014) predicted a shift from snowmelt-dominated runoff to

Published by Copernicus Publications on behalf of the European Geosciences Union. 2696 D. Freudiger et al.: Large-scale analysis of rain-on-snow events a more variable snow- and rain-fed regime in the future in North Atlantic Oscillation, temperature anomalies in De- Switzerland. These meteorological changes are very likely to cember 2010 reached –4 ◦C in central and northern Europe influence the occurrence and magnitude of RoS events, and (Lefebvre and Becker, 2011), and record snowpacks were ob- Köplin et al. (2014) predict a diversification of flood types in served nearly all over Germany for this time of the year (e.g. the wintertime as well as an increase of RoS flood events in Böhm et al., 2011; LHW, 2011; Besler, 2011). January 2011 the future in Switzerland. then brought thawing temperatures in combination with rain- Although Merz and Blöschl (2003) observed that 20 % of fall events, and from 6 to 16 January very high flows were the flood events in Austria were RoS-driven during the period observed at nearly all German gauging stations (e.g. Böhm 1971–1997 and hence showed the importance of such events et al., 2011; Bastian et al., 2011; Karuse, 2011; LHW, 2011; in central Europe, only few studies have specifically anal- Fell, 2011; Besler, 2011). Kohn et al. (2014) identified the si- ysed the changes of the frequency of RoS events over time multaneous occurrence of rainfall and snowmelt as the driv- and especially over large areas. Ye et al. (2008) observed an ing factor for those flood events, which led, beside other im- increase in RoS days in northern Eurasia, which they were pacts, to a restriction of navigation on the river Rhine and able to correlate with the observed increase in air tempera- large inundations in the lower Elbe river basin. The aims of ture and rainfall in the wintertime. Sui and Koehler (2001) this study are therefore (i) to derive criteria for RoS-driven attributed an increase in peak flows in the northern Danube events that have the potential to cause floods, using the case tributaries in Germany to an increase in RoS events, based study of January 2011 in Germany, and (ii) to analyse the on the combination of decreasing SWE and increasing maxi- changes in frequencies and magnitudes of these types of mum daily winter precipitation sums they found at a number events during the time period 1950–2011 in six major cen- of climate stations in the area. McCabe et al. (2007) found tral European river basins, i.e. Rhine, Danube, Elbe, Weser, disparate trends in the western USA with generally positive Oder, and Ems. temporal trends of RoS events frequencies for high-elevation sites and negative trends for low-elevation sites. In these areas, the increase of temperature appears to affect the occur- 2 Materials and methods rence of snow, contributing therefore to a lower frequency of RoS events (McCabe et al., 2007). Similarly, Surfleet and 2.1 Study area Tullos (2013) predicted with a model experiment that an increase in air temperature due to climate change would lead to The study area embodies the six major river basins of the a decrease of high peak flow due to RoS events for low- and German fluvial network. Since only German streamflow middle-elevation zones, while at high-elevation bands these records were used, the basins of the rivers Rhine, Danube, kinds of events would increase. All these studies show the Elbe, Weser, Oder, and Ems are considered only upstream of correlation between the frequency of RoS events, the changes the most downstream station in German territory (Fig. 1). Ac- in air temperature, and the importance of the elevation range. cording to the Hydrological Atlas of Germany (HAD, Bun- They therefore stress the need for a more accurate trend anal- desanstalt für Gewässerkunde), the basins were divided into ysis of those events in the context of climate change in cen- alpine, upland, or lowland sub-basins. This classification is tral Europe, where discharges mainly depend on alpine and motivated by the elevation of the main tributaries, but is not mid-elevation tributaries. strictly guided by elevation as the main rivers drop quickly Previous studies differ on the definition of RoS events. to lower elevations. McCabe et al. (2007) and Surfleet and Tullos (2013) de- Only the basins of the rivers Rhine and Danube have an fined an event as RoS-driven if simultaneously rainfall oc- “alpine” section in this classification. The alpine portion of curs, maximum daily temperature is greater than 0 ◦C, and the Rhine encompasses the basin ca. above Basel, and be- a decrease in snowpack can be observed; while for Ye et al. sides the entire basin area in Austria and Switzerland with (2008), a RoS event takes place only when at least one of four high mountains up to 4000 m a.s.l. it also includes the south- daily precipitation measurements is liquid and the ground is ern Black Forest with elevations of only up to 1500 m a.s.l. covered by ≥ 1 cm of snow. Sui and Koehler (2001) found The alpine section of the Danube basin consists also of a that most RoS events in southern Germany occurred when small part in the Black Forest near the source, but then in- snowmelt was larger than the rainfall depth. These definitions cludes mainly the southern tributaries of the Danube from the allow identifying all possible RoS events but are insufficient Alps. They comprise the river Inn, which originates from the if one focusses on the events that can effectively cause flood Swiss and Austrian Alps with elevations over 3000 m a.s.l., events. as well as a number of tributaries from the northern range of Due to the great hydrologic impact that RoS events can the Alps along the German–Austrian border with elevations have, there is a real need for assessing the changes in fre- below 3000 m a.s.l. quencies of those RoS events that may generate large floods. All river basins contain upland areas. These stretch A good example of such an event is the flood in January 2011 from near the southern border of Germany to the southern in central Europe. During a strong negative phase of the boundary of the northern German lowlands, as well as in the

Hydrol. Earth Syst. Sci., 18, 2695–2709, 2014 www.hydrol-earth-syst-sci.net/18/2695/2014/ D. Freudiger et al.: Large-scale analysis of rain-on-snow events 2697

tions to the peaks are not expected to change the relative ranking and hence the results of the trend analysis, and the discharge data were found suitable for this study. To assess the accuracy of the data, all data included in this analysis passed a visual quality control.

2.3 Estimation of snowpack and snowmelt

Snow accumulation and melt were estimated based on daily E-OBS mean temperature and precipitation sum data for the entire study area and are given in mm SWE. Precipitation is ◦ assumed to be solid if air temperature Ta < 1 C and liquid ◦ if Ta ≥ 1 C. Snowmelt M (mm) is estimated using a temperature index model, which assumes a relationship between ablation and air temperature (Eq. 1; e.g. Finsterwalder and Schunk, 1887; Collins, 1934; Corps of Engineers, 1956).

M = Mf · (Ta − Tb) (1) Figure 1. Study area: delimitation of the basin boundaries of the Martinec and Rango (1986) calculated degree-day fac- Rhine, Danube, Elbe, Weser, Oder, and Ems basins and subdivi- tors M for open areas depending on the snow density sion into alpine, upland, and lowland. The background raster corre- f of the snowpack. They suggested Mf values from 3.5 to sponds to the E-OBS data set. Gauging stations at the outlet of each ◦ −1 −1 sub-basin are represented with blue dots. 6 mm C day and even smaller for fresh snow. They also observed that Mf increases over the melt period. Hock (2003) listed Mf values for snow in high-elevation areas ◦ − − northern part of the Czech Republic (Elbe basin). The land- between 2.5 and 6 mm C 1 day 1. For sake of simplicity scape can be described as upland with elevation ranges from of the large-scale analysis, a constant conservative value ◦ −1 −1 200–300 m a.s.l. to up to Feldberg, 1493 m a.s.l., the highest of Mf = 3 mm C day was chosen for the entire study mountain in Germany outside the Alps. area and melt period. This value was found to represent the With the exception of the Danube, which is only consid- area well, since snow melts very fast in upland and low- ered to the German border, all river basins contain a lowland regions in Germany and the snowpack consists there- land section. These areas in northern Germany and western fore mainly of fresh snow. The base temperature Tb repre- Poland (Oder basin) are mainly constituted of lowland areas sents the threshold temperature for melting snow. Most stud- ◦ with altitudes ranging from 0 to 200 m a.s.l. ies set Tb to 1 C, since energy is needed to bring the snow ◦ to 0 C to start melting (e.g. Hock, 2003). Tb was therefore 2.2 Meteorological and hydrometric data set to 1 ◦C. The sensitivity of the subsequent trend calcula- tion to the choice of Tb and Mf was tested ranging from 0 ◦ ◦ −1 −1 Daily mean temperature and precipitation sums were ob- to 2 C for Tb and from 2 to 5 mm C day for Mf. Both tained from the European Climate Assessment and Dataset parameters were found to have an impact on the calculated project (ECA&D, http://www.ecad.eu) and the EU-FP6 snow depth but to be rather insensitive for the trends calcu- project ENSEMBLES (http://ensembles-eu.metofﬁce.com). lation, since the trend analysis considers relative changes to The so-called E-OBS data set (version 6.0) was interpolated the mean (Kohn et al., 2014). ◦ ◦ from climate stations all across Europe into a 0.25 × 0.25 For every grid cell, daily SWE of the snowpack was cal- regular latitude–longitude grid (Fig. 1; Haylock et al., 2008). culated for day i as the sum of the SWE of the day before The time series are available from 1 January 1950 to 31 De- and the snowmelt M (mm) or snowfall S (mm SWE) of the ◦ cember 2011 and cover the study area 46.00–55.25 N, 5.25– actual day (Eq. 2) and is given in mm SWE. 19.75◦ E. ( Daily mean discharge data from more than 300 gauging SWEi−1 + Si, if Ta < Tb SWEi = (2) stations (Fig. 2) in Germany were provided by German pub- SWEi−1 − Mi, if Ta ≥ Tb lic authorities. Details on the assembled data set can be found in Kohn et al. (2014). The time series are of different lengths, Snowpack was estimated for a period from 2 to 1 August but most of them cover the period 1950–2011. Since author- of the following year. Since August is the month with the ities usually correct peak discharge values with hydraulic least likely snow accumulation, SWE was re-set to zero on modelling or revise rating curves during the years after a 2 August of each year. Therefore the model only accounts ﬂood event, some of the most recent data used in this study for annual snow and no multi-year snow is taken into account were raw (as yet uncorrected) data. However, later correc- in the high alpine areas. The results show the winter period www.hydrol-earth-syst-sci.net/18/2695/2014/ Hydrol. Earth Syst. Sci., 18, 2695–2709, 2014 2698 D. Freudiger et al.: Large-scale analysis of rain-on-snow events

Figure 2. Large-scale analysis of the RoS event of January 2011. (a–f) Mean basin-wide daily snowpack, rainfall, and snowmelt (mm SWE) from 1 to 31 January, as well as the percentage of snow-covered cells. Map: return period and occurrence period of the maximum daily discharge in the calender year 2011 at all gauging stations (modified from Kohn et al., 2014). from 1 November to 31 May taking into account potential 3. Snowmelt M: the amount of M must be large enough snow season extents in the entire study area. As snow mea- compared to R; otherwise the event may be rather rain- surements in Germany are available in few locations only, the driven. calculated SWE was compared by (Kohn et al., 2014) to the products of the snow model SNOW4 (Germany’s National The time and magnitude of a flood driven by a RoS event Weather Service, DWD), which is based on the interpolation also depend on the response time of a basin. In this study we of ground-based snow measurements, for the winter 2010– distinguish between a RoS day and a RoS event. A RoS day 2011. A frequency analysis was performed on the occurrence is defined as a day when all hydrometeorologic conditions and amount of snow per area every day, and both model out- (R, SWE, and M) for a RoS event are met. A RoS event al- puts were found to be very similar. ways starts with a RoS day and may contain RoS days and non-RoS days. A RoS event lasts from the initial RoS day 2.4 Definition of RoS events to the day when the maximum discharge is observed after the first or after additional RoS days and within an assumed maximum response time following a RoS day. A RoS event The aim of this study is to identify those RoS events in with several RoS days is then considered as one event, even time series of rainfall occurrence and snowpack existence if it consists of multiple flood waves. We then defined the that have the potential to cause floods. Thus selection criteria equivalent precipitation depth P of an event as correspond- need to be defined. The general variables for a RoS-driven eq ing to the sum of daily rainfall and snowmelt during the RoS runoff generation event are as follows: event. The 2011 RoS event in Germany is a good example of the 1. Rainfall R: the amount of R must be substantial, other- flood-generation potential of such events. Based on the re- wise the event may be only snowmelt-driven. analysis of this 2011 RoS event in Germany (Kohn et al., 2014), selection criteria in the form of threshold values for the variables described above were defined. For the reanal- 2. Snowpack SWE: SWE needs to be large enough to be ysis, the return periods of the annual maximum daily dis- able to substantially contribute to runoff. charge at all available gauging stations were calculated with

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Table 1. Historical RoS events (sources: Wetterchronik, 2001; Kohn et al., 2014).

Date Province Basin Event description 18 Mar 1970 Lower Saxony Elbe Snowmelt and rainfall led to flooding all over the river, especially in Uelzen and Lüneburg. 27–28 Feb 1987 Bavaria Danube Large flooding due to snowmelt and incessant rainfalls in Schambachtal. 20 Jan 1997 Rhineland-Palatinate Rhine Small flooding after a snow-rich January and a very wet February. 6–10 Jan 2011 Central Europe Western basins: First wave of large-scale flooding due to snow-rich December 2010 Rhine, Weser, Ems followed by thawing temperatures in January 2011. 11–16 Jan 2011 Central Europe All basins Second wave of large-scale flooding due to snow-rich December 2010 followed by thawing temperatures in January 2011. the generalised extreme value distribution and the parame- sion with time and are expressed in percent to the mean value ters were estimated with the maximum likelihood method of the time series. This allows comparing the importance of (Venables and Ripley, 2002). This allowed proving the im- the changes in time in one basin with the changes in other portance of the associated flood peaks. To clearly identify the basins. The statistical significance of the trends was tested flood event as RoS-driven, the measured peak discharge dur- at a 5 % significance level using the non-parametric Mann– ing the event was then compared to rainfall, modelled snow Kendall test (Mann, 1945). Trends were calculated and com- depth, and modelled snowmelt for each sub-basin, which al- pared for the time periods 1950–2011 and 1990–2011, here- lowed defined threshold values for R, SWE, and M. Addi- after referred to as long-term and short-term trends. tionally, documented historical events, for which RoS processes were identified in the literature as the main cause for flooding within the study area, are listed in Table 1. These 3 Results kinds of events are overall not well documented and the information comes mostly from diverse textual information 3.1 Reanalysis of the large-scale RoS event in sources, but it gives us the location and the day of occurrence January 2011 in central Europe of past RoS floods. This information was used to “validate” The return periods of January 2011 peak flows illustrate the the selection criteria for RoS events that have been set on the severity of large-scale flooding across Germany (Fig. 2g). flood event of January 2011, since it allows checking if the Maximum annual daily discharge was observed from 6 to criteria are representative for other past events. 16 January at all gauging stations except in the northern part To compare P with the observed river discharge of RoS eq of the Elbe lowland sub-basin and in the Danube alpine sub- events that caused floods at the sub-basin scale, 12 gauging basin. With few exceptions discharge peaks reached at least stations were selected (Fig. 1). In the case of nested basins, a 1–2-year flood level, with large areas being affected by 20– the difference in discharge between the lower and upper sta- 50-year floods along the main rivers and a few exception tion was considered. No discharge data were available for the with 100-year floods in headwaters. Since two distinct dis- Oder basin outside Germany; therefore only one station at charge peaks were observed at nearly all gauging stations, the the outlet of the lowland sub-basin was considered. Finally, flood can be described as a two-wave flood event that spread the probability distribution of the daily discharge values was from west to east. Figure 2a–f further shows the evolution of classified into quantiles for each month and sub-basin. This the mean basin-wide daily R, SWE, and the percentage of expression gives an overview of the seasonal anomaly of snow-covered grid cells in the Rhine, Danube, Elbe, Weser, RoS-driven peak discharge values. The 0.5 quantile repre- Ems, and Oder river basins during the flood event. On 5 Jan- sents the median, and the closer to 1 the quantile is, the higher uary 2011, snow covered 100 % of the grid cells of the study is the discharge and the higher is its flood-generating poten- area and the mean SWE varied from 25 mm (Ems) to 70 mm tial. (Danube). The discharge peaks correspond very well to two phases of rainfall combined with snowmelt, and the event 2.5 Trend analysis was therefore identified as a RoS-driven flood. During the first flood wave (W1, from 6 to 10 January), −1 For all alpine, upland, and lowland sub-basins, the Peq, the mean basin R of 2–10 mm day fell on the western basins corresponding observed peak discharge, as well as the other (Fig. 2a, c, d), while in the eastern basins R never ex- variables influencing the occurrence of RoS events – namely ceeded 2 mm day−1 (Fig. 2b, d, f). W1 generated in total R, S, SWE, and M – were analysed for temporal trends. Peq between 51 and 71 mm in the western basins Rhine, These trends were calculated as the slope of a linear regres- Weser, and Ems, and between 22 and 48 mm in the eastern www.hydrol-earth-syst-sci.net/18/2695/2014/ Hydrol. Earth Syst. Sci., 18, 2695–2709, 2014 2700 D. Freudiger et al.: Large-scale analysis of rain-on-snow events basins Danube, Elbe, and Oder. In both regions the snowmelt all river basins but the Ems, where all snow was already content in Peq exceeded 25 %. Rain and snowmelt played melted after W1. The average basin rainfall depth was at an equally important role in the western basins, whereas least 2 mm, and the average basin snowmelt was at least 25 % snowmelt played the most important role in the eastern of Peq. We therefore chose conservative threshold values of basins. 3 mm for rainfall, 10 mm SWE for snowpack, and 20 % for During the second wave (W2, from 11 to 16 January), the snowmelt amount in Peq to define a RoS day. During the mean basin R reached 0–10 mm day−1 in the western basins 2011 event, the longest flood wave lasted 6 days (W2), and and 2–17 mm day−1 in the eastern basins. W2 generated in therefore the maximum response time of all basins was set to total Peq between 27 and 48 mm in the western basins, and 6 days. Thus, the duration of a RoS flood event is limited to between 49 and 26 mm in the eastern basins. On 10 January, 6 days after the last RoS day. most of the snow had already melted in the northwestern Figure 3 shows Peq for all RoS events (R ≥ 0 mm, SWE > part of Germany and W2 was therefore rather rain-driven in 0 mm, M > 0 %), potentially flood-generating RoS events this area, especially in the Ems river basin, where the second according to the criteria above (R ≥ 3 mm, SWE > 10 mm, flood wave was only rain-driven since all snow was already M > 20 %), and documented historical RoS-driven flood melted at this time. However, the snowpack was still substan- events against the corresponding measured discharge for all tial at the time in central Germany. After W2, nearly all snow river sub-basins. Most of the sample “all events” have only was melted in the Ems, Weser, and Oder basins. In the Rhine little impact on the discharge and will not cause floods or are and Danube river basins, most of the remaining snow was more rain-driven than rain-on-snow-driven and are therefore located in the alpine region. not of interest for this analysis. The selection of RoS events In Fig. 2a–f the cumulative Peqs are also compared for according to the above threshold values reveals that most all sub-basins according to their elevation classification. The of the RoS events in the alpine sub-basins have the poten- alpine sub-basins of the Rhine and Danube produced on tial to generate floods, while in the lowland sub-basins only average 4 mm day−1 equivalent precipitation depth during few events fall into this category. The criteria R ≥ 3 mm, W1 and W2, which was only half of the other sub-basins. SWE > 10 mm, and M > 20 % were able to select all doc- However, on 13 January the cumulative equivalent precipi- umented historical RoS-driven flood events (Table 1) except tation depth increased by 21 mm in the Danube alpine sub- for those of W1 in the lowland sub-basins of Oder and Elbe in basin. The upland sub-basins reacted very strongly to the January 2011. Less than 3 mm of rain fell in total, while the −1 RoS events, with Peq of almost 25 mm day during W1 in high temperatures generated more than 25 mm of snowmelt all basins and especially in the west. The Weser upland ar- in these sub-basins. Thus, W1 was rather snowmelt-driven eas were once again strongly affected during W2. After W2, than RoS-driven in the lowland sub-basins, but it was RoS- nearly all the grid cells were free of snow. During W1 Peq driven at the scale of the whole Oder and Elbe basins. was mostly caused by snowmelt at all elevation ranges in the Figure 3 also gives the correlation coefficients between Peq east and showed very similar reaction for all lowland and up- and the corresponding measured peak discharges for each land sub-basins. W2 resulted in a very fast increase of the sub-basin. The correlation shows how strongly runoff gener- cumulative Peq within few days in the east, especially for the ation is RoS-driven. The higher the correlation, the more the Elbe and Danube upland sub-basins (Fig. 2b, f). The Weser discharge is influenced by RoS events. The alpine and up- and Ems lowland sub-basins, in the western half of Germany, land sub-basins of the Rhine, Weser, and Danube showed the were also strongly impacted during W1, since the amount of highest positive correlation, with coefficients between 0.68 snow was substantial and unusual, and it had nearly com- and 0.75. In the other upland sub-basins Elbe and Ems, cor- pletely melted by the end of W1. W2 therefore had only relation coefficients of 0.48 and 0.51 were found, and in all little impact on these elevation ranges in these sub-basins lowland sub-basins none of the correlation coefficients was (Fig. 2a, c). The Rhine basin usually has a lot of snow during higher than 0.48. A few large events in Fig. 3h–l suggest that the wintertime, due to its larger upland elevation ranges and a RoS event can emphasise a flood event if discharge is al- the influence of its alpine part. For this reason, there were ready high at the time of occurrence. not many differences in the snowmelt processes of the Rhine The analysis of the discharge quantiles that correspond to lowland and upland sub-basins, and both elevation ranges the selected potentially flood-generating RoS events further were strongly impacted by both RoS flood waves. supports these differences. Figure 4 shows the percentage of RoS event in each month’s quantile range. In the alpine 3.2 Criteria for potentially flood-generating RoS events sub-basins of the Rhine and Danube, all selected RoS events correspond to high discharges (quantiles of 0.7–1) for every Selection criteria for RoS events that have the potential to month except May. The percentage of events in the highest cause floods were chosen based on the reanalysis of the discharge class (quantiles of 0.9–1) is large for all winter RoS-driven flood event in January 2011 in central Europe months, and progressively increasing from March to May, (Sect. 3.1). At the beginning of each flood wave, W1 and which means that the RoS events led to very high daily dis- W2, the average basin SWE had reached at least 10 mm in charges for the given months in these areas. In the upland

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Figure 3. Total equivalent precipitation depth and corresponding peak discharge for all possible RoS events (SP > 0 mm SWE, M > 0 %, PL ≥ 0 mm), for all potentially flood-generating events (SP > 10 mm SWE, M > 20 %, PL ≥ 3 mm), and for documented historical RoS- driven floods. The correlation coefficient R is given for the potentially flood-generating RoS events. sub-basins, RoS events occurred from December to April, winter 1950–1951 to 2010–2011. The trends were calcu- with most events in January–March again in the highest dis- lated only from years with RoS events and therefore rep- charge class (quantiles of 0.9–1). Only few events corre- resent the change in the magnitude of RoS events. In the spond to discharge quantiles < 0.7, confirming the strong alpine sub-basins of the Rhine and Danube, RoS events of flood-generating potential of the selected RoS events in this the whole winter season generated Peq between 100 and elevation range. In the lowland sub-basins, correspondence 600 mm year−1. This corresponds on average to 45, 22, and between RoS events and discharge quantiles is more het- 72 % of the total winter, early winter, and late winter precip- erogeneous. RoS events occurred only from December to itation (rain and snow) respectively. In both basins Peq was March and had corresponding peak discharges of all quan- greater in late winter than in early winter. No clear trends tiles, which supports the observations from Fig. 3 that RoS were identified in the magnitude for Peq of the early winter events do not necessarily cause the highest floods in these re- season, but the late winter season showed decreasing mag- gions, the discharge being mostly rain-driven. However, in nitudes over time, also leading to decreasing trends for the the Weser and Ems lowland sub-basins, RoS events were entire winter. Table 2 shows the frequency of RoS events very infrequent, but the few events that occurred between for time slices of 10 years for the early and late winter sea- December and March led mostly to relatively high discharge sons as the fraction of the total number of the RoS events peaks (quantiles of 0.8–1). that occurred within the period 1950–2011. On average, one- third of the RoS events occurred in the early winter as op- 3.3 Trends in magnitude and frequency of RoS events posed to two-thirds in the late winter in the alpine basins. In the Danube river sub-basin, early winter events became Figure 5 shows the annual sum of Peq of all selected RoS more frequent in the period 1990–2011 than in 1950–1990. events according to the thresholds described in Sect. 3.2 over In the Rhine sub-basins, no changes in RoS frequency were the entire winter season, the early winter season (November– observed between the two time periods. February), and the late winter season (March–May) from www.hydrol-earth-syst-sci.net/18/2695/2014/ Hydrol. Earth Syst. Sci., 18, 2695–2709, 2014 2702 D. Freudiger et al.: Large-scale analysis of rain-on-snow events

a) Rhine b) Danube 0 0 0.1 0.1 30 0.2 0.2 0.3 0.3 0.4 0.4 20 0.5 0.5 0.6 0.6 Alpine 0.7 0.7 10 0.8 0.8 Quantile of Q (−) 0.9 0.9 1 1 0 N D J F M A M N D J F M A M (%)

c) Rhine d) Danube e) Elbe f) Weser g) Ems 0 0 0 0 0 0.1 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.2 0.3 0.3 0.3 0.3 0.3 0.4 0.4 0.4 0.4 0.4 0.5 0.5 0.5 0.5 0.5 0.6 0.6 0.6 0.6 0.6

Upland 0.7 0.7 0.7 0.7 0.7 0.8 0.8 0.8 0.8 0.8 Quantile of Q (−) 0.9 0.9 0.9 0.9 0.9 1 1 1 1 1 N D J F M A M N D J F M A M N D J F M A M N D J F M A M N D J F M A M

h) Rhine i) Oder j) Elbe k) Weser l) Ems 0 0 0 0 0 0.1 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.2 0.3 0.3 0.3 0.3 0.3 0.4 0.4 0.4 0.4 0.4 0.5 0.5 0.5 0.5 0.5 0.6 0.6 0.6 0.6 0.6

Lowland 0.7 0.7 0.7 0.7 0.7 0.8 0.8 0.8 0.8 0.8 Quantile of Q (−) 0.9 0.9 0.9 0.9 0.9 1 1 1 1 1 N D J F M A M N D J F M A M N D J F M A M N D J F M A M N D J F M A M

Figure 4. Percentage of potentially ﬂood-generating RoS events from 1950 to 2011 by month of occurrence (November–May) and corresponding peak discharge quantile.

In the upland river sub-basins, RoS events generated max- 70 mm year−1 in the Oder basin to up to 250 mm year−1 in −1 imum annual sum of Peq from 90 mm year in the Ems the Rhine basin (Fig. 5h–l), corresponding to an average basin to up to 400 mm year−1 in the Danube basin (Fig. 5c– of 13, 18, and 29 % of the total winter, early winter, and g), corresponding to an average of 21, 28, and 35 % of the late winter precipitation respectively. Since the occurrence entire winter, early winter, and late winter precipitation re- of RoS events is infrequent, they depend on very specific spectively. The Danube sub-basin showed decreasing trends meteorological conditions and can occur either in the early in the magnitude of RoS events for the early and late win- or late winter seasons. The Rhine lowland showed the largest ter seasons. In the Rhine and Weser sub-basins, the magni- Peq of RoS events in the winter season (Fig. 5h), due to the tude of the RoS events increased in the late winter season runoff contribution from a small part of the basin located and decreased or remained constant in the early winter sea- in the medium-elevation mountain ranges. For all lowland son. The strong increasing trend in late winter in the Rhine sub-basins except the Oder, the magnitude of the events de- upland basin is influenced by a large RoS event that oc- creased in the late winter season. In the early winter sea- curred in the 1980s. In the Elbe sub-basin, both early and son, the magnitude increased in the Rhine, Weser, and Ems late winter seasons showed increasing trends in the magni- sub-basins and decreased in the Oder and Elbe sub-basins tude of the RoS events. In the Ems upland sub-basin, RoS (Fig. 5h–l). Comparing the period 1950–1990 to 1990–2011 events were rare and occurred mostly only during the early in the lowland sub-basins, RoS events became less frequent winter season. A decreasing trend in the magnitude of those in both the early and late winter seasons (Table 2). events was observed (Fig. 5g). In all upland sub-basins, RoS events occurred more often in the early winter season (on 3.4 Trends in RoS compounds and discharge average 70 % of all RoS events) than in the late winter season (30 %, Table 2). While the frequency of RoS events in In Fig. 6 long-term trends of the rainfall and snowfall sums, the early winter season remained constant between the peri- of the average SWE, of the total equivalent precipitation ods 1950–1990 and 1990–2011, the late winter events in all depths of all possible RoS days (R ≥ 0 mm, SWE > 0 mm, upland sub-basins became less frequent in the second time M > 0 %), of the selected potentially flood-generating RoS period. days (R ≥ 3 mm, SWE > 10 mm, M > 20 %), and of the cor- In the lowland basins, RoS events were rare and responding peak discharge are shown in percent change per generated maximum equivalent precipitation depths from year relative to the mean of the time period. The trends were

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a) Rhine b) Danube

)

−1 600 500 500 400 400 Winter 300 300 Early winter

Alpine 200 200 100 100 Late winter Eq. prec. depth (mm year 0 0 1950/51 1980/81 2010/11 1950/51 1980/81 2010/11

c) Rhine d) Danube e) Elbe f) Weser g) Ems

) 400 80

−1 150 250 250 300 200 200 60 100 150 150 200 40

Upland 100 50 100 100 20 50 50 Eq. prec. depth (mm year 0 0 0 0 0 1950/51 1980/81 2010/11 1950/51 1980/81 2010/11 1950/51 1980/81 2010/11 1950/51 1980/81 2010/11 1950/51 1980/81 2010/11

h) Rhine i) Oder j) Elbe k) Weser l) Ems 100 ) 250 80

−1 100 200 60 80 60 80 150 60 40 60 40 40 100 40 Lowland 20 20 50 20 20 Eq. prec. depth (mm year 0 0 0 0 0 1950/51 1980/81 2010/11 1950/51 1980/81 2010/11 1950/51 1980/81 2010/11 1950/51 1980/81 2010/11 1950/51 1980/81 2010/11

Figure 5. Total equivalent precipitation depth for all selected RoS events in the winter (November–May), in the early winter (November– February), and in the late winter (March–May) for the period 1950–2011. Only the years with RoS events are represented.

Table 2. Percentage of RoS events (1950–2011) in each sub-basin that occurred during time slices of 10 years during the early and late winter seasons. The italicised columns highlight the period 1990–2011, thus corresponding to the short-term trend analysis performed for RoS magnitudes.

Early winter Late winter 50/51 60/61 70/71 80/81 90/91 00/01 50/51 60/61 70/71 80/81 90/91 00/01 Period – – – – –– –––– –– 59/60 69/70 79/80 89/90 99/00 10/11 59/60 69/70 79/80 89/90 99/00 10/11 ALP Rh 6.9 7.9 6.2 5.8 7.9 6.6 8.6 12.4 9.8 9.8 9.0 9.2 ALP Do 4.3 1.9 4.1 4.3 5.5 5.5 11.9 13.6 10.4 12.2 13.0 13.2 UPL Rh 2.1 21.3 11.7 17.0 8.5 14.9 2.1 6.4 3.2 10.6 0.0 2.1 UPL El 11.0 15.4 7.7 14.3 8.8 8.8 3.3 13.2 3.3 7.7 1.1 5.5 UPL We 11.5 19.2 2.6 14.1 10.3 12.8 3.8 10.3 5.1 6.4 0.0 3.8 UPL Do 12.2 15.6 11.7 8.9 11.1 10.6 4.4 8.3 4.4 6.1 2.2 4.4 UPL Em 20.0 15.0 10.0 10.0 5.0 15.0 10.0 0.0 0.0 10.0 0.0 5.0 LOW Rh 2.7 13.3 9.3 22.7 8.0 10.7 4.0 10.7 2.7 12.0 0.0 4.0 LOW Od 8.0 12.0 4.0 12.0 8.0 12.0 8.0 12.0 8.0 12.0 0.0 4.0 LOW El 13.6 9.1 9.1 22.7 0.0 27.3 4.5 4.5 4.5 4.5 0.0 0.0 LOW We 15.4 15.4 0.0 23.1 0.0 15.4 7.7 0.0 7.7 7.7 0.0 7.7 LOW Em 5.6 11.1 5.6 11.1 0.0 11.1 16.7 11.1 11.1 5.6 0.0 11.1

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R S SWE Peq Discharge Sum Sum Mean All RoS days All RoS days ALP Rh * * * * * * * 10 Do * * * * * * * * * * * UPL Rh * * * * * * * * * * * * El * * * * * * * * * * 8 We * * * * * * * * Do * * * * * * * * * * * * * 6 Em * * * * * Od * * * * * * * * * * * LOW Rh * * * * * * * * * * * * * * 4 El * * * * * We * * * * * * Em * * * * * 2 Od * * * * * * * * * * * N D J F M A M W N D J F M A M W N D J F M A M W N D J F M A M W N D J F M A M W 0 Days R > 3 mm Days S > 0 mm SWE Days SWE > 10 mm flood-generating RoS days flood-generating RoS days

ALP Rh * * * −2 Do * * * * * * * * * * Trend relative to mean (%) UPL Rh * * * * * * * El * * * * * * * * * * * −4 We * * * * * * Do * * * * * * * * * Em * * −6 Od * * * * * * * * LOW Rh * * * * * * * −8 El * * * * * * We * * * Em * * * * * * * −10 Od * * * * * * * * N D J F M A M W N D J F M A M W N D J F M A M W N D J F M A M W N D J F M A M W

Figure 6. Comparison of the long-term trends (1950–2011) of the total equivalent precipitation depth, the snow water equivalent, the snowfall, and the rainfall for the individual months November–May (N–M) and the winter season (W) for the alpine (ALP), upland (UPL) and lowland (LOW) sub-basins of the Rhine (Rh), Danube (Do), Elbe (El), Weser (We), Oder (Od), and Ems (Em). Trends are given as the yearly change relative to the mean of the period 1950–2011. Statistically significant trends at p < 5 % are shown with a red star. calculated for the individual months from November to May trends in the number of days with SWE > 10 mm SWE were and for the sum over the entire winter season for all basins. identified in the alpine regions. In the alpine sub-basins, the In contrast to Fig. 5, the trends were calculated including trends in Peq were overall positive during the early winter years without RoS events and thus also account for changes season and negative in April and May. In the upland sub- in the frequency of occurrence. For R around 20 % of the basins the trends Peq were positive in January and February trends were statistically significant, for S 30 %, and for mean and negative from March to May. In the lowland sub-basins SWE 42 %. For the sample of all events, around 10 % of the these trends were negative for all winter months. The trends trends in Peq and 17 % of the trends in discharge were statis- in Peq for the selected RoS days were very similar to those tically significant at p < 0.05, while for the selected poten- for all RoS days in the alpine and upland sub-basins, but the tially flood-generating events only around 2 % of the trends lowland trends differed with positive trends from November were statistically significant. Overall, the detected long-term to January. The trends in corresponding peak discharges were trends range between −4 and +4 % for all variables. R in- very similar to the trends in Peq, with slightly more positive creased in November, December, and April in the alpine sub- values for the entire winter season for all basins and elevation basins and from January to March in the upland and lowland ranges except for the Ems and Oder sub-basins, where trends sub-basins. In contrast, S showed overall decreasing trends. were negative. Similar to S, SWE decreased for all elevation ranges and all Compared to the long-term trends in Fig. 6, the short-term winter months, with especially large negative trends in April trends (Fig. 7) overall showed stronger negative and posi- in some upland and all lowland basins. Similarly, the number tive trends for all variables ranging from less than −10 % to of days with SWE > 10 mm SWE decreased between Jan- more than +10 %. A maximum of 20 % of all trends were uary and April in the upland and lowland sub-basins, espe- statistically significant. Opposite to the long-term trends, the cially in April in the Ems and Weser sub-basins, indicating a short-term trends in R and in the occurrence of days with shortening of the winter duration in these regions. No clear a rainfall sum of at least 3 mm were positive in February

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R S SWE Peq Discharge Sum Sum Mean All RoS days All RoS days ALP Rh * * 10 Do * * * * UPL Rh * * * * * El * * * * * * 8 We * * * * * Do * * * * 6 Em * * * * * * Od * * * * LOW Rh * * * * * * * 4 El * * * * * * * * We * * * * * * * Em * * * * * * 2 Od * * * * * * * N D J F M A M W N D J F M A M W N D J F M A M W N D J F M A M W N D J F M A M W 0 Days R > 3 mm Days S > 0 mm SWE Days SWE > 10 mm flood-generating RoS days flood-generating RoS days

ALP Rh * −2 Do * * * * * Trend relative to mean (%) UPL Rh * El * * −4 We * * * Do * * * Em * * −6 Od * * LOW Rh * * * −8 El * * * * * We * * * * Em * * * * * −10 Od * * N D J F M A M W N D J F M A M W N D J F M A M W N D J F M A M W N D J F M A M W

Figure 7. Comparison of the short-term trends (1990–2011) of the total equivalent precipitation depth, the snow water equivalent, the snowfall, and the rainfall for the individual months November–May (N–M) and the winter season (W) for the alpine (ALP), upland (UPL) and lowland (LOW) sub-basins of the Rhine (Rh), Danube (Do), Elbe (El), Weser (We), Oder (Od), and Ems (Em). Trends are given as the yearly change relative to the mean of the period 1990–2011. Statistically significant trends at p < 5 % are shown with a red star. and May and negative in the rest of the winter for all basins. The sensitivity analysis of the base temperature showed ◦ Also opposite to the long-term trends, short-term trends in S that increasing or decreasing Tb by ±1 C had little impact were positive from November to March and negative in April on the direction of the trends. On average, 95 % of the cal- in all upland and lowland sub-basins. The alpine sub-basins culated trends showed the same direction. The Peq of the se- showed, in contrast, negative trends in S for the long-term lected potentially flood-generating RoS days was the most and short-term periods. The same differences are reflected in sensitive with still around 80 % of the trends having the same SWE, with high positive short-term trends from December to direction. Rainfall trends were the least sensitive, with 100 % March, only negative trends in May in the upland and low- showing the same direction. The calculated trends were also land sub-basins, and negative trends for all winter months insensitive to the degree-day factor Mf when testing values ◦ −1 −1 in the alpine sub-basins. Trends in the Peq of all RoS days ranging from 2 to 5 mm C day . This low sensitivity can were negative in the alpine sub-basins for all winter months, be explained by the fact that the trend analysis considers the but the trends in potentially flood-generating RoS days were relative changes to the mean. mostly positive. In the upland and lowland sub-basins, trends were negative in November, December, and April and positive from January to March, and a particularly strong increase 4 Discussion in the Peq of the selected RoS days was observed from Jan- uary to March. This increase was also reflected in the trends The RoS-driven flood event that spread over Germany and of the corresponding peak discharge in all upland and low- central Europe in January 2011 is a good example of the land sub-basins. In January and February, the trends in dis- large-scale impact that RoS events can have. From 6 to charge had a similar direction to the trends in Peq but were 16 January nearly all gauging stations in Germany observed smaller. the maximum water level in 2011. On the one hand, the large- scale impact of this RoS event was due to the extremely www.hydrol-earth-syst-sci.net/18/2695/2014/ Hydrol. Earth Syst. Sci., 18, 2695–2709, 2014 2706 D. Freudiger et al.: Large-scale analysis of rain-on-snow events widespread snow cover over the study area in the beginning tion is to identify basin-scale processes (Merz and Blöschl, of January, and its remarkable depth with extreme values at 2003). The conceptual temperature index model employed several locations in Germany (e.g. Böhm et al., 2011; Bastian in this study allowed estimating the potential snowpack and et al., 2011; Karuse, 2011; LHW, 2011; Fell, 2011; Besler, snowmelt. Even when the degree-day factor was generalised 2011). The snowpack therefore represented a very large wa- for the entire study area, the method led to a good estimation ter reservoir available for runoff. On the other hand, the cli- of the equivalent precipitation depth, was accurate enough matic conditions with thawing temperatures and rainfall in to recognise known historical events, and was supported by January provided the required energy to melt the snowpack. the comparison to measured peak discharges during the RoS Runoff was therefore generated during a very short time, event. This validation of RoS events and the selection and with a maximum of 6 days for each flood wave, and simul- analysis of potential flood-generating RoS events add to pre- taneously reached the upper and lower parts of the Rhine, vious studies, which have mostly looked only at RoS days. Danube, Weser, Elbe, Oder, and Ems basins, thus causing Using the January 2011 RoS-driven flood events as a ref- floods in most areas. Even if most of these discharges corre- erence, it was therefore possible to identify the magnitude of spond to return periods of less than 10 years and thus are not rainfall, the snowpack, and the percentage of snowmelt in the statistically extreme (Kohn et al., 2014), this RoS event em- equivalent precipitation depth as the main characteristics of phasises the large-scale impact of such events and their po- a RoS event and as the major characteristics for runoff gen- tential of shifting the annual peak flow from the late winter eration at the large scale. The resulting threshold values of season to early winter season. This event therefore represents 3 mm for rainfall, 10 mm SWE for snowpack, and 20 % for a good reference for the characterisation of RoS events with snowmelt content in Peq were able to detect all documented flood-generation potential. historical RoS-driven flood events in the time series and The runoff generation from RoS events is influenced by to specifically select only potentially flood-generating RoS many antecedent conditions and physical processes such as events. These thresholds have therefore proved to be good the thermal, mass, and wetness conditions of the snowpack, indicators for RoS-driven flood events. The snowpack thresh- or the snow metamorphism, the water movement through old (10 mm SWE) is not only representative for the event of the wet snow, the interaction of melt water with underly- January 2011, but also corresponds to the definition of the ing soil, or the overland flow at the snow base (Singh et al., beginning of the winter by Beniston (2012) and Bavay et al. 1997; Marks et al., 1998). A physically based model would (2013). The advantage of the approach of identifying RoS be needed to continuously simulate the development of the events with threshold values is that it can easily be applied snowpack as well as evapotranspiration, sublimation, and in- to other basins where discharge measurements are available, filtration, and thus to estimate the actual runoff generation. In and it represents a useful tool for analysing changes in fre- a large-scale analysis however, parameterisation for all pro- quencies and magnitudes of those events. cesses would be difficult. The almost continental scale of the The results showed an elevation dependence of RoS events study requires considering data availability and conceptual- in all basins, confirming the observations of different previ- isation of processes dominant at that scale. In the case of ous studies (e.g. Merz and Blöschl, 2003; Pradhanang et al., this study, these are the hydrometeorological magnitude of 2013). RoS events generally have a high impact on discharge rain-on-snow events and the temporal scale relevant to flood peaks in alpine and upland basins. These events are most generation at the large scale. The aim of this study is there- likely to lead to high discharges (quantiles of 0.7–1 in the fore not to improve the description or understanding of runoff alpine sub-basins and even 0.8–1 in the upland sub-basins), generation at the hillslope or small catchment scale during a and they therefore have a real potential for generating floods RoS event, but to analyse RoS events’ long-term evolution in these regions. This result is in agreement with the ob- at the large scale. Therefore, no runoff is calculated, but the servation of Sui and Koehler (2001) that RoS events play equivalent precipitation depth is related to the RoS event by a more important role in runoff generation than pure rainfall its comparison to measured peak discharge during the event. events for topographical elevations above about 400 m a.s.l. However, even at the small catchment scale, Rössler et al. during the wintertime. In all lowland sub-basins, the quan- (2014) concluded that the hydrometeorological conditions tile ranges are strongly influenced by the antecedent condi- are the main factors quantifying RoS-driven flood events. tions of the stream in the wintertime, which is due to the fact Despite its apparent simplicity compared to energy bal- that winter floods are rain-dominated in these areas, since ance methods, Ohmura (2001) showed that the temperature- snowfall occurs only infrequently. In the lowland sub-basins, based melt index model was sufficiently accurate for most winter floods strongly depend on antecedent moisture con- practical purposes, and was justified on physical grounds ditions (soil saturation and groundwater tables; Nied et al., since the air temperature is the main heat source for the at- 2013). Therefore RoS events do not necessarily cause floods mospheric longwave radiation. This model has the advan- in these regions, but they can exacerbate a flood. For exam- tage that it needs only daily precipitation and temperature ple, the Elbe river basin generated discharges corresponding data, often the only available data, and has already proved to return periods of up to 100 years during the January 2011 to be accurate enough for large-scale modelling if the inten- event not only because of the RoS event but also because of

Hydrol. Earth Syst. Sci., 18, 2695–2709, 2014 www.hydrol-earth-syst-sci.net/18/2695/2014/ D. Freudiger et al.: Large-scale analysis of rain-on-snow events 2707 the very wet autumn 2010, which led to already very high sured discharges of RoS events were positive from January water levels and discharges at the beginning of January (e.g. to March in the alpine and upland sub-basins, and especially Kohn et al., 2014). in March for the short-term trend analysis, suggesting an im- One challenge in the trend analysis of extreme RoS events pact of this increasing magnitude. is the censored data; i.e. events do not occur every year. Most Trends have to be interpreted carefully since they depend methods for trend analysis try to statistically disclose out- on the choice of the time period, which can be influenced by liers, as for example the Sen slope method. In our case, how- many climatic factors and also by extreme values. The anal- ever, the outliers are often exactly the values that need to be ysis of long-term (1950–2011) vs. short-term (1990–2011) considered. Therefore, linear regression was found to be the trends showed different, even opposite, results for all vari- method better suited for the trend analysis. The zeros also ex- ables. Overall, long-term trends are smaller than short-term plain why many trends were not statistically significant. This trends. The greatest difference between both periods is in the is a well-known problem in hydrology. Kundzewicz et al. trend in the mean SWE. In the long-term analysis, snowpack (2012) observed for example that the strong natural variabil- has declined in all basins, while it has increased in the short- ity of hydrologic events can alter trend detection, and IPCC term period in all basins except the alpine sub-basins. Fricke (2012) pointed out that, due to the fact that extreme events (2006) observed that the average snowpack in Germany for are per definition rare, long record lengths are required to al- the period 1961–1990 was substantially higher than for the low for detection of trends in extremes. However, the lack of period 1991–2000. The 21st century was characterised by statistical significance does not mean that the trends do not extreme events. The winter 2005–2006 and December 2010, exist, but that the hypothesis of no existing trends could not for example, were identified as extremely snow rich in Ger- be rejected. As discussed, e.g., by Stahl et al. (2010) in more many (Fricke, 2006; Pinto et al., 2007; Böhm et al., 2011). detail, the application of trend tests has been criticised ex- This explains the differences in the trends, since the extreme tensively in the literature because many assumptions are not events of the 21st century will have more weight in a shorter met by hydrological time series data. As suggested in other time series, especially if they occurred in the beginning of large-scale studies, a systematic regional consistency of trend the period such as for the lower observed snow depth. direction and magnitude is therefore a more relevant result The alpine sub-basins show different trends to the upland than the number of statistical significances. In this study, the and lowland sub-basins. While the upland and lowland sub- value of the trend analysis has its main value not in the abso- basins have negative trends in the long-term analysis and pos- lute numbers estimated but in the comparison of the consis- itive trends in the short-term analysis, SWE in the alpine sub- tency in the trends of the individual components involved in basins decreased in both the long- and short-term trend anal- rain-on-snow events. yses. This difference can be explained by the climatic condi- The estimated magnitudes and frequencies revealed a dif- tions specific to the alpine regions, which are very different ferent importance of RoS events in the different elevation to those in the upland and lowland sub-basins. For example, zones represented by the sub-basins. Nearly half of the to- while exceptionally great SWE was measured all over Ger- tal winter precipitation (rain and snow) and even two-thirds many in December 2010, the Swiss Alps experienced snow- of the late winter precipitation contribute to RoS events in packs below average (e.g. Trachte et al., 2012; Techel and the alpine sub-basins, while this contribution is one-third in Pielmeier, 2013). In another study in the Swiss Alps, Benis- the upland sub-basins, and only one-fifth in the lowland sub- ton (2012) found that the wintertime precipitation declined basins. The largest changes in frequencies were observed in between 15 and 25 % over the 1931–2010 period and that the upland basins, where late winter RoS events have be- the number of snow-sparse winters has increased in the last come less frequent since the 1990s. This change in frequen- 40 years, while the number of snow-abundant winters has de- cies can be explained by the decreasing trends in snow depth clined. But in the meantime, some winters since the 1990s observed in the late winter season in these areas (Figs. 6 and have experienced record-breaking snow amounts and dura- 7) and therefore by a decreasing probability of rain falling on tions (Beniston, 2012). Rainfall also shows opposite trends, a snow cover in the late winter season. In contrast, the trends increasing for the long time series and mostly decreasing for in rainfall are positive in the early winter season, increas- the short time series in the wintertime. As snowpack and rain- ing the probability for RoS events, especially in January and fall both influence the occurrence of RoS events, trends in February. These results agree well with the observations of RoS days are therefore difficult to identify for the long-term many studies worldwide (e.g. Birsan et al., 2005; Knowles analysis, since rainfall is increasing but snow depth is de- et al., 2006; Ye, 2008; Ye et al., 2008). Trends in magni- creasing. tude vary from one basin to another. The upland Elbe and For upland and lowland sub-basins, the results of the long- Rhine sub-basins show positive trends in the early and late term analysis are opposite and show dominating positive winter seasons, while the other upland sub-basins have nega- trends in RoS days for the upland sub-basins and negative tive trends. This difference can be explained by the more fre- trends for the lowland sub-basins. In the short-term analysis quent and stable snow cover in the upland basins of the Elbe in contrast, clear positive trends are detected for all RoS days and Rhine. The corresponding positive trends in the mea- in upland and lowland regions. The trends for the selected www.hydrol-earth-syst-sci.net/18/2695/2014/ Hydrol. Earth Syst. Sci., 18, 2695–2709, 2014 2708 D. Freudiger et al.: Large-scale analysis of rain-on-snow events potentially flood-generating RoS days are even more posi- providers ECA&D project (http://www.ecad.eu) for providing tive, leading to the conclusion that they have become an im- precipitation and temperature data. The authors also thank the portant factor for the winter discharge and that the occurrence environmental agencies of the German federal states for providing of maximum peak flow from RoS events between January discharge data. Finally, the authors acknowledge two anonymous and March has become more frequent since the 1990s. reviewers for their thoughtful comments that helped improve the manuscript.

Edited by: G. Di Baldassarre 5 Conclusions

In a context of climate change, snowpack and precipitation References in the wintertime are very likely to change and therefore may influence the frequency and magnitude of the flood haz- Bastian, D., Göbel, K., Klump, W., Kremer, M., Lipski, P., and ard from rain-on-snow events in central Europe. The anal- Löns-Hanna, C.: Das Januar-Hochwasser 2011 in Hessen, Hy- ysis of causes and trends for past RoS events is challeng- drologie in Hessen, Heft 6, Hessische Landesamt für Umwelt und ing since these events depend on many influences. Defining Geologie, Wiesbach, Germany, 2011 (in German). threshold values to characterise RoS events allowed identify- Bavay, M., Grünewald, T., and Lehning, M.: Response of snow ing the events with potentially high impact on river discharge cover and runoff to climate change in high Alpine catchments on a large scale and analysing them for trends in frequency of Eastern Switzerland, Adv. Water Resour., 55, 4–16, 2013. Beniston, M.: Is snow in the Alps receding or disappearing?, WIREs and magnitude. The results showed an elevation dependence Clim. Change, 3, 349–358, doi:10.1003/wcc.179, 2012. of RoS events and suggest they have the strongest impacts Besler, C.: Dokumentation Elbehochwasser Januar 2011, Teil 1: in upland regions, where an increasing magnitude of these Meteorologische Situation und hydrologischer Verlauf des events was observed. However, the frequency of RoS events Hochwassers, Report, Staatliches Amt für Landwirtschaft und decreased in the second half of the time period 1950–2011 in Umwelt (StALU) Westmecklenburg, Schwerin, Germany, 2011 the late winter season in upland and lowland basins and can (in German). be related to decreasing trends in snowpack in the late winter Birsan, M.-V., Molnar, P., Burlando, P., and Pfaundler, M.: Stream- season. Increasing trends in rainfall in the early winter season flow trends in Switzerland, J. Hydrol., 314, 312–329, 2005. as well as increasing trends in equivalent precipitation depth Blöschl, G., Kirnbauer, R., and Gutknecht, D.: Modelling snowmelt during RoS events in some upland sub-basins suggest that in a mountainous river basin on an event basis, J. Hydrol., 113, these events have become more important at this elevation 207–229, 1990. Böhm, U., Fiedler, A., Machui-Schwanitz, G., Reich, T., and class. Schneider, G.: Hydrometeorolgische Analyse der Schnee- und The results show the importance of the choice of the anal- Tauwettersituation im Dezember 2010/Januar 2011 in Deutsch- ysed period for the detection of trends, with opposite trends land, Report, Deutscher Wetterdienst (DWD), Offenbach, Ger- found for snow water equivalent in the long-term and short- many, 2011 (in German). term periods. The 21st century has been affected by several Collins, E. H.: Relationship of degree-days above freezing to runoff, extreme events, which makes the analysis even more diffi- EOS T. Am. Geophys. Un., 15, 624–629, 1934. cult. As the example of January 2011 in Germany and cen- Corps of Engineers: Summary report of the snow investigations, tral Europe showed, rain can release a large amount of wa- snow hydrology, US Army Engineer Division (North Pacific, 210 ter stored in the snowpack and RoS events can cause very Custom House, Portland, Oregon), 437 pp., 1956. widespread flood events, delivering a large amount of water Fell, E.: Kurzbericht: Hochwasser im Rheingebiet – Januar 2011, to the streams within a very short time. If such events are Report, Landesamt für Umwelt Wasserwirtschaft und Gewer- beaufsicht (LUWG) Rheinland-Pfalz, Mainz, Germany, 2011 (in likely to become more frequent in the future in certain basins German). and elevation ranges, the winter flood hazard will increase. Finsterwalder, S. and Schunk, H.: Der Suldenferner, Zeitschrift des Therefore, there is a real need for an improved understanding Deutschen und Oesterreichischen Alpenvereins, 18, 72–89, 1887 of the relation between RoS events and flooding, and more (in German). analysis is needed on their occurrence at different scales. Floyd, W. and Weiler, M.: Measuring snow accumulation and ablation dynamics during rain-on-snow events: innovative measure- ment techniques, Hydrol. Process., 22, 4805–4812, 2008. Acknowledgements. In part, the study was funded by the Bun- Fricke, W.: Wieder mehr Schnee im Winter?, Global Atmosphere desanstalt für Gewässerkunde as part of a reanalysis of the Watch, Brief 33, Deutscher Wetterdienst (DWD), Germany, hydrological extremes during the year 2011. The article processing March 2006 (in German). charge was funded by the German Research Foundation (DFG) Garvelmann, J., Pohl, S., and Weiler, M.: From observation and the Albert Ludwig University Freiburg in the funding pro- to the quantification of snow processes with a time-lapse gramme Open Access Publishing. The authors thank J. U. Belz camera network, Hydrol. Earth Syst. Sci., 17, 1415–1429, for his support with data and advice. The authors would also like doi:10.5194/hess-17-1415-2013, 2013. to acknowledge the E-OBS data set from the EU-FP6 project ENSEMBLES (http://ensembles-eu.metoffice.com) and the data

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Haylock, M. R., Hofstra, N., Klein Tank, A. M. G., Klok, Merz, R. and Blöschl, G.: A process typology of regional floods, E. J., Jones, P. D., and New, M.: A European daily high- Water Resour. Res., 39, 1340, doi:10.1029/2002WR001952, resolution gridded dataset of surface temperature and pre- 2003. cipitation for 1950–2006, J. Geophys. Res., 113, D20119, Nied, M., Hundecha, Y., and Merz, B.: Flood-initiating catchment doi:10.1029/2008JD10201, 2008. conditions: a spatio-temporal analysis of large-scale soil mois- Hock, R.: Temperature index melt modeling in mountain areas, ture patterns in the Elbe River basin, Hydrol. Earth Syst. Sci., J. Hydrol., 282, 104–115, 2003. 17, 1401–1414, doi:10.5194/hess-17-1401-2013, 2013. IPCC: Summary for policymakers, in: Managing the risks of ex- Ohmura, A.: Physical basis for the temperature-based melt-index treme events and disasters to advance climate change adaptation. method, J. Appl. Meteorol., 40, 753–761, 2001. A special report of working groups I and II of the Intergovern- Pinto, J. G., Brücher, T., Fink, A. H., and Krüger, A.: Extraordinary mental Panel on Climate Change IPCC, Cambridge University snow accumulations over parts of central Europe during winter of Press, Cambridge, UK and New York, NY, USA, 3–21, 2012. 2005/06 and weather-related hazards, Weather, 62, 16–21, 2007. Karuse, P.: Gewässerkundlicher Monatsbericht Januar 2011, Re- Pradhanang, S. M., Frei, A., Zion, M., Schneiderman, E. M., Steen- port, Bayerisches Landesamt für Umwelt und Geologie (HLUG), huis, T. S., and Pierson, D.: Rain-on-snow events in New York, Wiesbaden, Germany, 2011 (in German). Hydrol. Process., 27, 3035–3049, 2013. Kattelmann, R. C.: Macropores in snowpacks of Sierra Nevada, Ann Renard, B., Lang, M., Bois, P., Dupeyrat, A., Mestre, O., Niel, H., Glaciol, 6, 272–273, 1985. Sauquet, E., Prudhomme, C., Parey, S., Paquet, E., Neppel, L., Kattelmann, R. C.: Flooding from rain-on-snow events in the Sierra and Gaillhard, J.: Regional methods for trend detection: Assess- Nevada, in: Destructive water: Water-caused natural disasters, ing field significance and regional consistency, Water Resour. their abatement and control, edited by: Leavesley, G. H., Pro- Res., 44, W08419, doi:10.1029/2007WR006268, 2008. ceedings of the conference, Anaheim, California, June 1996, Rössler, O., Froidevaux, P., Börst, U., Rickli, R., Martius, O., and IAHS Publication, 239, 59–65, 1997. Weingartner, R.: Retrospective analysis of a nonforecasted rain- Knowles, N., Dettinger, M. D., and Cayan, D. R.: Trends in snowfall on-snow flood in the Alps – a matter of model limitations or versus rainfall in the Western United States, J. Climate, 19, 4545– unpredictable nature?, Hydrol. Earth Syst. Sci., 18, 2265–2285, 4559, 2006. doi:10.5194/hess-18-2265-2014, 2014. Kohn, I., Freudiger, D., Rosin, K., Stahl, K., Weiler, M., and Singh, P., Spitzbart, G., Hübl, H., and Weinmeinster, H. W.: Hydro- Belz, J.: Das hydrologische Extremjahr 2011: Dokumentation, logical response of snowpack under rain-on-snow events: a field Einordnung, Ursachen und Zusammenhänge, Report, Mitteillung study, J. Hydrol., 202, 1–20, 1997. Nr. 29, Bundesanstalt für Gewässerkunde (Hrsg.), Koblenz, Ger- Stahl, K., Hisdal, H., Hannaford, J., Tallaksen, L. M., van Lanen, many, 2014 (in German). H. A. J., Sauquet, E., Demuth, S., Fendekova, M., and Jódar, J.: Köplin, N., Schädler, B., Viviroli, D., and Weingartner, R.: Season- Streamflow trends in Europe: evidence from a dataset of near- ality and magnitude of floods in Switzerland under future climate natural catchments, Hydrol. Earth Syst. Sci., 14, 2367–2382, change, Hydrol. Process., 28, 2567–2578, doi:10.1002/hyp.9757, doi:10.5194/hess-14-2367-2010, 2010. 2014. Sui, J. and Koehler, G.: Rain-on-snow induced flood events in Kundzewicz, Z. W., Plate, E. J., Rodda, H. J. E., Rodda, J. C., Southern Germany, J. Hydrol., 252, 205–220, 2001. Schnellnhuber, H. J., and Strupczewski, W. G.: Changes in flood Surfleet, C. G. and Tullos, D.: Variability in effect of climate change risk – setting the stage, in: Changes in Flood Risk in Europe, on rain-on-snow peak flow events in temperate climate, J. Hy- edited by: Kundzewicz, Z. W., IAHS Press, Wallingford, 11–26, drol., 479, 24–34, 2013. 2012. Techel, F. and Pielmeier, C.: Schnee und Lawinen in den Schweizer Lefebvre, C. and Becker, A.: Das Klima des Jahres 2011 im glob- Alpen, Hydrologisches Jahr 2010/11, Report, WSL-Institut für alen Massstab, Klimastatusbericht, Report, Deutscher Wetterdi- Schnee- und Lawinenforschung SLF, Davos, Switzerland, 2013 enst (DWD), Offenbach, Germany, 2011 (in German). (in German). LHW: Bericht über das Hochwasser Januar 2011, Report, Lan- Trachte, K., Obregón, A., Bissolli, P., Kennedy, J. J., Parker, D. E., desbetrieb für Hochwasserschutz und Wasserwirtschaft (LHW) Trigo, R. M., Barriopedro, D., Kendon, M., Prior, J., Achberger, Sachsen-Anhalt, Magdeburg, Germany, 2011 (in German). C., Gouvela, C., Sensoy, S., Hovsepyan, A., and Grigoryan, Mann, H. B.: Nonparametric test against trend, Econometrica, 13, V.: State of the Climate in 2011, Regional Climates – Europe, 245–259, 1945. B. Am. Meteorol. Soc., 93, 186–199, 2012. Marks, D., Kimball, J., Tingey, D., and Link, T.: The sensitivity of Venables, W. N. and Ripley, B. D.: Modern Applied Statistics Using snowmelt processes to climate conditions and forest cover during S, 4th Edn., Springer, New York, United States, 2002. rain-on-snow: a case study of the 1996 Pacific Northwest flood, Wetterchronik: http://www.wetterzentrale.de/cgi-bin/ Hydrol. Process., 12, 1559–1587, 1998. wetterchronik/home.pl, access: 14 June 2013, 2001. Martinec, J. and Rango, A.: Parameter values for snowmelt runoff Ye, H.: Changes in precipitation types associated with air tempera- modelling, J. Hydrol., 84, 197–219, 1986. ture over the northern Eurasia, J. Climate, 14, 3140–3255, 2008. McCabe, G. J., Clark, M. P., and Hay, L. E.: Rain-on-snow events in Ye, H., Yang, D., and Robinson, D.: Winter rain on snow and its as- the western United States, B. Am. Meteorol. Soc., 88, 319–328, sociation with air temperature in northern Eurasia, Hydrol. Pro- doi:10.1175/BAMS-88-3-319, 2007. cess., 22, 2728–2736, 2008.

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